Question

If sinƟ + cos Ɵ = √cos Ɵ, (Ɵ ≠ 900 ) then the value of tan Ɵ is (a) √2 - 1 (b) √2 + 1 (c) √2 (d) - √2​

Answer 1

Step-by-step explanation:

*Given:

$\sin( \theta) + \cos( \theta) = \sqrt{2}\cos( \theta),\quad( \theta \neq90°)$

To find: The value of $\tan( \theta)$ is

(a) √2 - 1

(b) √2 + 1

(c) √2

(d) - √2

Solution:

Tip:

$\bf \frac{ \sin \theta }{\cos \theta} = \tan\theta$

Step 1: Take the given trigonometric equation

$\sin( \theta) + \cos( \theta) = \sqrt{2}\cos( \theta)$

Step 2: Take $\cos( \theta)$ to RHS

${sin} \theta = \sqrt{2} \cos( \theta) - \cos( \theta)$

Step 3: Take $\cos( \theta)$ common from both terms in RHS

${sin} \theta = (\sqrt{2} - 1 ){cos}\theta$

Step 4: Take $cos \theta$ to LHS

$\frac{ \sin \theta }{\cos \theta} = \sqrt{2} - 1$

$\bold{\tan\theta = \sqrt{2} - 1}$

Final answer:

$\bold{\tan\theta = \sqrt{2} - 1}$

Option a is correct.

Hope it helps you.

Note*: Question is corrected.

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